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ehrlich-b/euclidean-jordan

Bryan Ehrlich

Palomar Registrypalomar/PALOMAR-2026-08-23-000006Aug 23, 2026math.RAscore 0

A Euclidean Jordan algebra is a finite-dimensional real inner-product space carrying a commutative bilinear product with a unit, satisfying the Jordan identity (x*y)*(x*x) = x*(y*(x*x)) and the associativity of the inner product = . This is Faraut-Koranyi's definition (Analysis on Symmetric Cones, III.1). This development formalizes the classical structure theory of these algebras. Mathlib carries the Jordan identity as the typeclass IsCommJordan together with five operator-commutation lemmas, and nothing beyond that: no idempotent theory, no Peirce decomposition, no spectral theory. This…

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